Jove
Visualize
Contact Us
JoVE
x logofacebook logolinkedin logoyoutube logo
ABOUT JoVE
OverviewLeadershipBlogJoVE Help Center
AUTHORS
Publishing ProcessEditorial BoardScope & PoliciesPeer ReviewFAQSubmit
LIBRARIANS
TestimonialsSubscriptionsAccessResourcesLibrary Advisory BoardFAQ
RESEARCH
JoVE JournalMethods CollectionsJoVE Encyclopedia of ExperimentsArchive
EDUCATION
JoVE CoreJoVE BusinessJoVE Science EducationJoVE Lab ManualFaculty Resource CenterFaculty Site
Terms & Conditions of Use
Privacy Policy
Policies

Related Concept Videos

BIBO stability of continuous and discrete -time systems01:24

BIBO stability of continuous and discrete -time systems

1.0K
System stability is a fundamental concept in signal processing, often assessed using convolution. For a system to be considered bounded-input bounded-output (BIBO) stable, any bounded input signal must produce a bounded output signal. A bounded input signal is one where the modulus does not exceed a certain constant at any point in time.
To determine the BIBO stability, the convolution integral is utilized when a bounded continuous-time input is applied to a Linear Time-Invariant (LTI) system....
1.0K
Entropy Change in Reversible Processes01:10

Entropy Change in Reversible Processes

3.3K
In the Carnot engine, which achieves the maximum efficiency between two reservoirs of fixed temperatures, the total change in entropy is zero. The observation can be generalized by considering any reversible cyclic process consisting of many Carnot cycles. Thus, it can be stated that the total entropy change of any ideal reversible cycle is zero.
The statement can be further generalized to prove that entropy is a state function. Take a cyclic process between any two points on a p-V diagram.
3.3K
Poisson's And Laplace's Equation01:25

Poisson's And Laplace's Equation

4.5K
The electric potential of the system can be calculated by relating it to the electric charge densities that give rise to the electric potential. The differential form of Gauss's law expresses the electric field's divergence in terms of the electric charge density.
4.5K
Linear Approximation in Frequency Domain01:26

Linear Approximation in Frequency Domain

412
Linear systems are characterized by two main properties: superposition and homogeneity. Superposition allows the response to multiple inputs to be the sum of the responses to each individual input. Homogeneity ensures that scaling an input by a scalar results in the response being scaled by the same scalar.
In contrast, nonlinear systems do not inherently possess these properties. However, for small deviations around an operating point, a nonlinear system can often be approximated as linear....
412
Reversible and Irreversible Processes01:14

Reversible and Irreversible Processes

6.0K
The thermodynamic processes can be classified into reversible and irreversible processes. The processes that can be restored to their initial state are called reversible processes. It is only possible if the process is in quasi-static equilibrium, i.e., it takes place in infinitesimally small steps, and the system remains at equilibrium However, these are ideal processes and do not occur naturally. An ideal system undergoing a reversible process is always in thermodynamic equilibrium within...
6.0K
Separable Differential Equations01:20

Separable Differential Equations

179
A separable differential equation is a type of first-order differential equation where the derivative dy/dx can be expressed as a product of two functions: one that depends only on x and another that depends only on y. This allows for the rearrangement of the equation so that all terms involving y are on one side, and all terms involving x are on the other. This process, known as the separation of variables, simplifies the process of solving the equation by enabling the integration of both...
179

You might also read

Related Articles

Articles linked to this work by shared authors, journal, and citation graph.

Sort by
Same author

Coherence properties of collective modes in ensembles of oscillators.

Physical review. E·2026
Same author

Internal reliability and antireliability in dynamical networks.

Physical review. E·2025
Same author

An Elementary Microscopic Model of Sympatric Speciation.

Theoretical biology forum·2025
Same author

Prestrain-induced contraction in one-dimensional random elastic chains.

Physical review. E·2022
Same author

Quantifying fairness to overcome selfishness: A behavioural model to describe the evolution and stabilization of inter-group bias using the Ultimatum Game.

Mathematical biosciences and engineering : MBE·2019
Same author

Plasma cortisol and ACTH levels in 416 VLBW preterm infants during the first month of life: distribution in the AGA/SGA population.

Journal of perinatology : official journal of the California Perinatal Association·2019
Same journal

Erratum: Low-dimensional model for adaptive networks of spiking neurons [Phys. Rev. E 111, 014422 (2025)].

Physical review. E·2026
Same journal

Disentangling the effects of many-body forces on depletion interactions.

Physical review. E·2026
Same journal

Charge transport and mode transition in dual-energy electron beam diodes.

Physical review. E·2026
Same journal

Optimization of multisite reactions in complex compartmentalized media.

Physical review. E·2026
Same journal

Origin of geometric cohesion in nonconvex granular materials: Interplay between interdigitation and rotational constraints enhancing frictional stability.

Physical review. E·2026
Same journal

Interaction of walkers with a standing Faraday wave.

Physical review. E·2026
See all related articles

Related Experiment Video

Updated: Mar 10, 2026

Inherent Dynamics Visualizer, an Interactive Application for Evaluating and Visualizing Outputs from a Gene Regulatory Network Inference Pipeline
10:44

Inherent Dynamics Visualizer, an Interactive Application for Evaluating and Visualizing Outputs from a Gene Regulatory Network Inference Pipeline

Published on: December 7, 2021

2.7K

Stochastic bifurcations in the nonlinear parallel Ising model.

Franco Bagnoli1, Raúl Rechtman2

  • 1Dipartimento di Fisica e Astronomia and CSDC, Università di Firenze, and INFN-Istituto Nazionale di Fisica Nucleare-Sezione di Firenze Via Giovanni Sansone 1, I-50019 Sesto Fiorentino, Italy.

Physical Review. E
|December 15, 2016
PubMed
Summary
This summary is machine-generated.

This study explores phase transitions in a nonlinear Ising model relevant to opinion formation. Long-range couplings induce spin synchronization and chaotic oscillations, revealing complex dynamics in network models.

More Related Videos

Finite Element Modelling of a Cellular Electric Microenvironment
08:23

Finite Element Modelling of a Cellular Electric Microenvironment

Published on: May 18, 2021

4.1K
Scalable Quantum Integrated Circuits on Superconducting Two-Dimensional Electron Gas Platform
05:39

Scalable Quantum Integrated Circuits on Superconducting Two-Dimensional Electron Gas Platform

Published on: August 2, 2019

10.4K

Related Experiment Videos

Last Updated: Mar 10, 2026

Inherent Dynamics Visualizer, an Interactive Application for Evaluating and Visualizing Outputs from a Gene Regulatory Network Inference Pipeline
10:44

Inherent Dynamics Visualizer, an Interactive Application for Evaluating and Visualizing Outputs from a Gene Regulatory Network Inference Pipeline

Published on: December 7, 2021

2.7K
Finite Element Modelling of a Cellular Electric Microenvironment
08:23

Finite Element Modelling of a Cellular Electric Microenvironment

Published on: May 18, 2021

4.1K
Scalable Quantum Integrated Circuits on Superconducting Two-Dimensional Electron Gas Platform
05:39

Scalable Quantum Integrated Circuits on Superconducting Two-Dimensional Electron Gas Platform

Published on: August 2, 2019

10.4K

Area of Science:

  • Statistical physics
  • Complex systems
  • Network science

Background:

  • The Ising model is a fundamental tool for studying magnetism and phase transitions.
  • Opinion formation models often utilize network structures to understand collective behavior.
  • Understanding synchronization and chaotic dynamics is crucial in complex systems.

Purpose of the Study:

  • To investigate phase transitions in a nonlinear Ising model with both linear antiferromagnetic and nonlinear ferromagnetic couplings.
  • To analyze the impact of network topology, specifically the small-world effect, on magnetization dynamics.
  • To explore bifurcations and synchronization phenomena induced by varying model parameters and network structures.

Main Methods:

  • Mean-field approximation to analyze chaotic oscillations.
  • Spatial modeling of the Ising model with rewiring to introduce long-range connections.
  • Examination of parameter changes including couplings, connectivity, dilution, and inhomogeneity.

Main Results:

  • Mean-field analysis reveals chaotic oscillations dependent on couplings and connectivity.
  • Spatial model exhibits bifurcations in average magnetization due to topology changes (small-world effect).
  • Long-range couplings induce spin synchronization, leading to coherent periodic and chaotic oscillations.

Conclusions:

  • The nonlinear Ising model displays complex dynamics, including chaotic oscillations and bifurcations, mirroring opinion formation processes.
  • Network topology significantly influences magnetization dynamics, with long-range connections promoting synchronization.
  • Model parameter variations, such as dilution and inhomogeneity, can induce novel bifurcation behaviors like 'bubbling'.